In this paper we propose {\it a region choice problem} for a knot projection. This problem is an integral extension of Shimizu's 'region crossing change unknotting operation.' We show that there exists a solution of the region choice problem for all knot projections.
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48 results for “region choice problems”
Problems on region choices for knot and link diagrams solved using Alexander numbering.
problem Existence of solutions for region choice problems on knot and link diagrams.
method Alexander numbering for regions, alternative proofs, necessary and sufficient conditions.
result Existence of solutions for region choice problems on link diagrams.
Generic smooth boundaries for isoperimetric regions in 8D manifolds.
problem Understanding boundaries of isoperimetric regions in high-dimensional spaces.
method Generic regularity results for isoperimetric regions in closed Riemannian manifolds of dimension eight.
result Smooth nondegenerate boundaries for isoperimetric regions for generic metrics and volumes.
Investigates consumption and investment strategies with preference for liquid assets.
problem Infinite horizon consumption-portfolio problem with liquid and illiquid risky assets.
method Analyzes properties of value function, categorizes solvency regions, and characterizes optimal policy.
result Liquidity preference leads to higher liquid wealth and lower consumption, potentially negative allocation to illiquid asset.
A trust-region method for stochastic variational inference with applications to streaming datastat.ML
Stochastic variational inference allows for fast posterior inference in complex Bayesian models. However, the algorithm is prone to local optima which can make the quality of the posterior approximation sensitive to the choice of hyperparameters and initialization. We address this problem by replacing the natural gradi…
Unified perspective on natural gradient methods for GMMs, improving variational inference.
problem Efficiently learning multi-modal approximations of complex distributions.
method Comparison and optimization of VIPS and iBayes-GMM methods for Gaussian mixture models.
result Hybrid approach significantly outperforms both VIPS and iBayes-GMM.
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within a specified interval. The complete algorithm---which dynamically chooses whethe…
A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options. To obtain an upper bound, we establi…
Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models efficiently. First-order methods such as gradient descent are usually the methods of choice for training machine learning models. However, these methods converge to saddle points for certain ch…
We propose a trust region method for policy optimization that employs Quasi-Newton approximation for the Hessian, called Quasi-Newton Trust Region Policy Optimization QNTRPO. Gradient descent is the de facto algorithm for reinforcement learning tasks with continuous controls. The algorithm has achieved state-of-the-art…
This survey article discusses three aspects of knot colorings. Fox colorings are assignments of labels to arcs, Dehn colorings are assignments of labels to regions, and Alexander-Briggs colorings assign labels to vertices. The labels are found among the integers modulo n. The choice of n depends upon the knot. Each typ…
Success Conditioning as Policy Improvement: The Optimization Problem Solved by Imitating Successcs.AI
Success conditioning optimizes policies by imitating successful trajectories, solving a trust-region optimization problem.
problem Improving policies through random actions that lead to desired outcomes.
method Success conditioning, which involves collecting and updating policies based on successful trajectories.
result Success conditioning solves a trust-region optimization problem, maximizing policy improvement with a divergence constraint.
This paper addresses pure gauge questions in the study of (asymptotically) de Sitter spacetimes. We construct global solutions to the eikonal equation on de Sitter, whose level sets give rise to double null foliations, and give detailed estimates for the structure coefficients in this gauge. We show two results which a…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to …
Study on bit threads and their locking properties in holographic spacetimes.
problem Understanding the conditions under which regions can be locked in holographic spacetimes.
method Investigation of different density bounds and their implications on the locking of regions.
result Non-crossing regions can be locked under the most stringent bound, but crossing regions cannot.
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by…
Dynamic regressor selection (DRS) systems work by selecting the most competent regressors from an ensemble to estimate the target value of a given test pattern. This competence is usually quantified using the performance of the regressors in local regions of the feature space around the test pattern. However, choosing …
The Fuzzy ROCstat.OT
The fuzzy ROC extends Receiver Operating Curve (ROC) visualization to the situation where some data points, falling in an indeterminacy region, are not classified. It addresses two challenges: definition of sensitivity and specificity bounds under indeterminacy; and visual summarization of the large number of possibili…
We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market practices than other approaches suggested in the literature. In addition, they are gi…
We analyze the dynamics of a forecasting game which exhibits the phenomenon of information cascades. Each agent aims at correctly predicting a binary variable and he/she can either look for independent information or herd on the choice of others. We show that dynamics can be analitically described in terms of a Langevi…
TROLL improves RL for LLMs by replacing clipping with a trust region projection.
problem Clipping in RL for LLMs causes instability and suboptimal performance.
method TROLL uses a discrete differentiable trust region projection to replace clipping, balancing computational cost and effectiveness.
result TROLL consistently outperforms PPO-like clipping in training speed, stability, and final success rates.
A new algorithm for solving constrained convex optimization problems efficiently.
problem Constrained convex optimization problems requiring high accuracy solutions.
method Second-Order Conditional Gradient Sliding (SOCGS) algorithm, using projection-free methods to solve quadratic subproblems inexactly.
result Converges quadratically in primal gap after a finite number of linearly convergent iterations.
To a region of the plane satisfying a suitable convexity condition we associate a knot concordance invariant . For appropriate choices of the domain this construction gives back some known knot Floer concordance invariants like Rasmussen's invariants, and the Ozsv\' ath-Stipsicz-Szab\' o upsilon invarian…
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.
Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single-possibly fragile-optimal design. Expensive black-box functions can be optimised effectively with Bayesian optimisation, where a Gaussian process is a popu…
PR-GNN identifies salient brain regions for ASD biomarkers.
problem Identifying brain regions associated with neurological disorders.
method Pooling Regularized Graph Neural Network (PR-GNN) with novel salient region selection.
result PR-GNN outperforms baseline methods in ASD classification accuracy.
Paper proposes a method to estimate consumer valuations from bundle sales data.
problem Estimating consumer valuations from bundle sales data using classical methods is challenging.
method Proposes an approach using EM algorithm and Monte Carlo simulation to estimate consumer valuations from bundle sales data.
result The approach can recover the distribution of consumers' valuations and is robust to unobserved no-purchases and clustered market segments.
Mirror descent method improved RL algorithms.
problem Improving RL algorithms for better performance.
method Mirror descent method applied to RL, solving trust-region problems.
result MDPO outperforms or matches other RL algorithms in continuous control tasks.
Near-future large galaxy surveys will encounter blended galaxy images at a fraction of up to 50% in the densest regions of the universe. Current deblending techniques may segment the foreground galaxy while leaving missing pixel intensities in the background galaxy flux. The problem is compounded by the diffuse nature …
Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD class…
Fast Calculation of the Knowledge Gradient for Optimization of Deterministic Engineering Simulationscs.CE
A novel efficient method for computing the Knowledge-Gradient policy for Continuous Parameters (KGCP) for deterministic optimization is derived. The differences with Expected Improvement (EI), a popular choice for Bayesian optimization of deterministic engineering simulations, are explored. Both policies and the Upper …
We present a framework to derive upper bounds on the number of regions that feed-forward neural networks with ReLU activation functions are affine linear on. It is based on an inductive analysis that keeps track of the number of such regions per dimensionality of their images within the layers. More precisely, the info…
New insights into how neural networks classify data.
problem Understanding the topological structure of decision regions in ReLU networks.
method Defining generic and transversal ReLU networks, and using linear complexes to identify obstructions.
result Generic, transversal ReLU networks have at most one bounded connected component in their decision regions.
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers recently. More precisely, given a local volatility surface and a choice of stocha…
Unified framework for data-free sampling using Wasserstein gradient flows.
problem Efficient sampling from unnormalized distributions without data.
method Unified theoretical framework based on Wasserstein gradient flows.
result Unified form of velocity field for various f-divergences.
The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both strike and time, how to…
Given a point (the "spider") on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the "fly" - the reflection of the spider across the center of the box). Without loss of generality, we can assume that the box has dimensions with the spider on one …
Investors target specific regions of payoff distributions for portfolio optimization.
problem Optimizing portfolio performance across different return distribution regions.
method Developed a dynamic portfolio-choice framework targeting downside or upside quantiles.
result Policies focused on downside regions provide stronger left-tail protection and higher Sharpe ratios.
Phase coexistence in a forecasting gamephysics.soc-ph
Individual choices are either based on personal experience or on information provided by peers. The latter case, causes individuals to conform to the majority in their neighborhood. Such herding behavior may be very efficient in aggregating disperse private information, thereby revealing the optimal choice. However if …
EPICSCORE improves conformal scores by explicitly accounting for epistemic uncertainty.
problem Overconfident predictions in data-sparse regions due to lack of epistemic uncertainty.
method Model-agnostic approach using Bayesian techniques like Gaussian Processes, Dropout, and Regression Trees.
result Enhanced predictive intervals that adaptively expand in sparse data regions and maintain compact intervals in abundant data.
The specificty and sensitivity of resting state functional MRI (rs-fMRI) measurements depend on pre-processing choices, such as the parcellation scheme used to define regions of interest (ROIs). In this study, we critically evaluate the effect of brain parcellations on machine learning models applied to rs-fMRI data. O…
Two new algorithms solve nonconvex-strongly concave problems efficiently.
problem Solving nonconvex-strongly concave minimax problems.
method Proposed MINIMAX-TR and MINIMAX-TRACE algorithms.
result Find -second order stationary points within iterations.
Bayesian optimization tackles constrained high-dimensional problems with penalties and trust regions.
problem Constrained optimization in high-dimensional black-box settings with expensive evaluations and complex feasibility regions.
method Penalty formulation, surrogate model, trust region strategy, Expected Improvement acquisition function.
result The proposed Trust Region method identifies high-quality feasible solutions with fewer evaluations and maintains stable performance.
To ensure stability of learning, state-of-the-art generalized policy iteration algorithms augment the policy improvement step with a trust region constraint bounding the information loss. The size of the trust region is commonly determined by the Kullback-Leibler (KL) divergence, which not only captures the notion of d…
The paper investigates how target normalization and momentum affect dying ReLUs in neural networks.
problem Understanding and mitigating the dying ReLU problem in neural networks.
method Empirical analysis and theoretical modeling of a discrete-time linear autonomous system.
result Target variance plays a crucial role in the dying ReLU phenomenon, and momentum exacerbates this issue.
Adam achieves optimal convergence in deep ReLU networks via novel Kakeya bounds.
problem Training deep ReLU networks using Adam in non-smooth settings.
method Stratified Morse theory and Kakeya bounds to analyze region crossings and convergence.
result First global-optimal convergence for Adam in non-smooth, non-convex ReLU landscapes.
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias.…
We introduce a variant of the -nearest neighbor classifier in which is chosen adaptively for each query, rather than supplied as a parameter. The choice of depends on properties of each neighborhood, and therefore may significantly vary between different points. (For example, the algorithm will use larger $k…